Semiparametric Full Likelihood Inference For The Size Of Population From Capture-Recapture Data

Capture-recapture methods are widely used cost-effective sampling techniques for estimating population sizes which are very important quantities in the fields of ecology,demography,software engineering,public health and epidemiology.Most of the exist-ing estimation methods in the literature are based on conditional likelihoods and inverse weighting estimating equations.The resulting inverse probability weighting estimators,also known as Horvitz-Thompson type estimators,might not be stable since some weight-s might be quite small.What's more,the corresponding Wald type confidence intervals may have severer undercoverage and lower limits can be smaller than the observed sample size.These shortcomings motivate us to develop an estimation method with better per-formance.Considering that full likelihood usually has many nice properties,we combine conditional likelihoods and empirical likelihood in this dissertation,and further develop a series of semiparametric full likelihood inference approaches to estimating the population sizes.Compared with the conventional estimating methods,the effects of the proposed approaches are significantly improved.Capture-recapture data are roughly divided into two categories:continuous time capture-recapture data and discrete time capture-recapture data.For continuous time capture-recapture data,we use the Andersen-Gill intensity model to build the relation-ship between the capture intensity and individual covariates,and consider fixed effect model and mixed effect model.Handling with the distribution of covariates by empirical likelihood,we propose a semiparametric full likelihood inference approach to the popula-tion size based on the continuous time capture-recapture data.We prove the asymptotic normality and the semiparametric efficiency of the maximum empirical likelihood esti-mator,and prove the asymptotic chi-square distribution of the empirical likelihood ratio statistics.Compared with the conditional-likelihood-based Horvitz-Thompson estima-tor,the proposed maximum empirical likelihood estimator has a smaller mean square error and the empirical likelihood ratio confidence interval has a more accurate coverage probability with lower limit always no less than the sample sizeFor discrete time capture-recapture data,we use the Huggins-Alho model to build the relationship between the capture probability and the individual covariates.Here we focus on the cases with missing covariates and propose a semiparametric full likelihood inference approach to the population size under the missing at random mechanism.We investigate the asymptotic properties of the maximum empirical likelihood estimator and the empirical likelihood ratio statistics,and illustrate the efficiency of these estimators by simulation studies and real-world data analyses.It is worthwhile to mention that compared with the conventional inverse probability weighting and multiple imputation methods,the proposed semiparametric full likelihood method does not need to make any parametric or nonparametric assumptions about the selection probability,so that the estimation results are more robust to the possible misspecification of the selection probability.Lastly,we incorporate the individual behavioral factor into the Huggins-Alho model and propose a semiparametric full likelihood inference method for the population size un-der a general model.We investigate the asymptotic properties of the maximum empirical likelihood estimator and the empirical likelihood ratio statistics,and illustrate the impact of individual behavioral factor on the proposed estimators through numerical analyses.